Abstract We give a new derivation for the properties of radiation appearing to an observer bounded in a space-time domain that has a horizon; this includes the Rindler case (constant accelerating frame) and the Schwarzschild solution (black hole). Because of the global nature of the quantum state, which inevitably extends to space beyond the horizon, it is possible for the observer to gather information concerning the physical state beyond his horizon, similar to the Einstein-Podolsky-Rosen experiments. Depending on the quantum states, the radiation can appear to be either black-body or something quite different.